Numerical evaluation of Kramers—Kronig relations

Abstract

Optical rotatory dispersion and circular dichroism are closely connected phenomena. Their interdependency is contained in the Kramers-Kronig relations which are, just as thermodynamic relations, of a very fundamental nature. As a matter of fact they apply to every physical system, where the response to an action from outside is linear and where the principle of causality holds. This means that the system does not squeal before it is hurt. For our purpose it is of interest to realize that the relations imply that a complete knowledge of circular dichroism as a function of frequency contains the same in­formation as a complete knowledge of rotary dispersion. However, our knowledge about the two effects is always limited to a small region of the spectrum only. A region that extends from 200 to 800 nm, say. Therefore it is of great importance to use the Kramers-Kronig relations in order to derive as much information as possible from the two types of measurements together at the available wavelengths.